Calderglen Mathematics Department Blue Course Revision Sheets Block F BF1 Brackets, equations and inequalities BF2 Pythagoras’ Theorem and Significant Figures BF3 Scientific Notation, Indices and Surds BF4 Statistics, graphs, charts and probability BF5 Rotations and transformations
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Calderglen Mathematics Department
Blue Course
Revision Sheets
Block F
BF1 Brackets, equations and inequalities
BF2 Pythagoras’ Theorem and Significant Figures
BF3 Scientific Notation, Indices and Surds
BF4 Statistics, graphs, charts and probability
BF5 Rotations and transformations
BF1 Brackets, Equations and Inequalities
BF1.1 I have revised the use of algebraic shorthand.
BF1.2 Substitution into expressions involving negative numbers.
1. Evaluate when and .
2. Evaluate when and .
3. Evaluate
when , and .
BF1.3 I can multiply out brackets of the form: ( )ax bx cy
Multiply out the brackets:
1. 2.
3. 4.
BF1.4 I can multiply out brackets of the form : ( )( )ax by cx dy
Multiply out the brackets:
1. 2.
3. 4.
5. 6.
.
BF1.5 I can multiply out brackets of the form : 2( )( )ax b cx dx c
Multiply out the brackets:
1. 2.
BF1.6 I can multiply out brackets in more complex expressions and gather
like terms.
Simplify:
1.
2.
BF1.7 I can solve equations that contain brackets.
Solve:
1.
2.
BF1.8 I can solve equations which contain fractions.
Solve:
1.
2.
.
.
BF1.9 I can solve inequalities which may contain a change of direction of
inequality sign.
Solve:
1. 2.
BF1.10 I can use equations and inequalities to make mathematical models
1. The shape shown below is made from a small rectangle cut from a larger
rectangle. If the shaded area is 87 square centimetres, find the value of x.
2. The heights of 10 plants were measured as 5cm, 3cm, 4cm, xcm, 5cm, 3cm,
xcm, xcm, 2cm, 5cm.
a) Write down an expression in x for the mean height of a plant.
b) If the mean height of the plants is greater than 3∙9cm.
Write down an inequality for the above information and solve it for x.
c) Explain your answer to b) in the context of this problem
BF2 Pythagoras and Significant Figures
BF2.1 I can use Pythagoras to find the length of a hypotenuse
Calculate the length of the missing side in each triangle:
a)
b)
c)
x
15
8
x
4∙5
20
x
12 12
BF2.2 I can use Pythagoras to find the length of a shorter side
Calculate the length of the missing side in each triangle:
a)
b)
c)
10
x
8
60
x
50
4.8
x
1∙4
BF2.3 I can use Pythagoras to solve problems
1. In the isosceles
triangle shown, find
the length of AB
2. For the kite shown, find
the length of the side
marked x.
3. Fairy lights are strung
across a river in the shape
of an isosceles triangle with
a base length of 60 metres.
If the length of the string of fairy lights is 90 metres, calculate the width of
the river to the nearest centimetre.
60m
16m
A
B C
27∙5cm
18cm
36∙5cm x
12
m
12∙5m
A B
BF2.4 I can use Pythagoras to find the distance between two coordinate
points
On squared paper plot these pairs of points and calculate the distance between them.
a) O ( 0 , 0 ) and M ( 8 , 6 ) b) P ( 1 , 2 ) and Q ( 9 , 8 ) c) R ( 3 , 6 ) and S ( 8 , -6 )
BF2.5 I can use the Converse of Pythagoras to prove or disprove that a
triangle is right angled.
1. Use the Converse of Pythagoras to decide which of these triangles are
right angled:
a)
b)
c)
4
3∙1
2.4
25
24
7
15
9
12
BF2.6 I can apply the theorem of Pythagoras to construct mathematical
models of real life situations.
1. A rope has to be fed through a pipe in the ground for the telephone wire to
be connected from the house to the telephone pole.
John has a 40 metre
long rope to complete
the job.
Is the rope long enough?
You must justify your answer with appropriate working.
2. A loop of rope is used to mark
out a triangular plot, PQR.
The loop of rope measures 24 metres.
Pegs are positioned at P and Q such that PQ is 10 metres.
The third peg is positioned at R such that QR is 8 metres.
Prove that angle PRQ = 90 .
Do not use a scale drawing.
P Q
R
Pipe
Telephone
Pole
30 m
25 m
House
House
3. The top of a crane is in the shape of a triangle, shown as PQR.
PQ = 39m, PR = 15m, RQ = 36m.
(a) Prove that angle PRQ is a right angle.
(b) Hence calculate the area of PQR .
(c) Calculate the length of altitude RM.
P M
39m
Q
R
36m 15m
BF2.7 I can round to a specified number of significant figures
1) Round each of these numbers correct to 2 sig fig.
a) 49483 b) 365∙4 c) 1∙789 d) 7∙77
2) Round each of these numbers correct to 1 sig fig.
a) 44 b) 6∙08 c) 0∙909 d) 17∙5
3) Complete the following calculations and give your answers correct to 3 sig
fig.
a) 17 ÷ 9
b) 7% of £125000
c) Find the circumference of a circle with diameter 4.15cm
4) A plane departs Newtown and flies 65 miles north followed by 40 miles
west, as shown, until it reaches Rivercity.
Calculate the direct distance from Newtown to Rivercity, giving your
answer to 3 significant figures.
Newtown
Rivercity
65 miles
40 miles
BF1 Scientific Notation, Indices and Surds
BF3.1 I can convert large and small numbers to and from scientific notation.
1. Write the following numbers in Scientific Notation:
a) 8,000 b) 70,000 c) 5,600 d) 72,000
e) 6,700,000 f) 8,250,000 g) 38,600,000 h) 6,700
i) 42,000,000 j) 3,810 k) 6,340 l) 700
m) 943 n) 32,000,000 o) 7,321 p) 627
q) 8,125 r) 720 s) 173,100,000 t) 15,562,000
u) 176,000,000 v) 324,000,000 w) 464,000 x) 17
2. Write the following numbers in Scientific Notation:
a) 4 million b) 12 million c) 6∙5 million
d) 9½ million e) 8∙46 million f) 5¼ million
g) 68∙75 million h) 12¾ million i) 23∙648 million
3. Write the following numbers out in full:
a) b) c)
d) e) f)
g) h) i)
j) k) l)
m) n) o)
p) q) r)
4. Write the following numbers in Scientific Notation:
a) 0.0071 b) 0.00024 c) 0.000031 d) 0.000057
e) 0.00076 f) 0.0241 g) 0.00382 h) 0.000711
i) 0.0000324 j) 0.00675 k) 0.000038 l) 0.00028
m) 0.0000629 n) 0.000054 o) 0.00000068 p) 0.0005002
5. Write the following numbers out in full:
a) b) c)
d) e) f)
g) h) i)
j) k) l)
m) n) o)
p) q) r)
6. Write the following numbers in Scientific Notation: